New correlation relations in classical and quantum systems with different numbers of subsystems1

Abstract

Abstract We present a review of the general approach to the problem of correlations in classical statistics and quantum statistics of systems with different numbers of subsystems and demonstrate the information-entropic relations for systems without subsystems recently obtained for Shannon entropies. We present the example of a single-qudit state corresponding to the N-level atom, consider explicitly the qutrit state, and show that qutrit can be interpreted as a set of several qubits. For each of these qubits, there exist corresponding von Neumann entropies, and constraints for these entropies determine the hidden correlations between the qubits in spite of the fact that the qutrit does not contain any subsystem. These constraints are expressed in terms of nonnegativity of the mutual information introduced, which usually exists only for the states of systems with subsystems. The value of information parameterizes the hidden correlations of artificial qubits in the system. We discuss examples of some qudits.